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Find the measure of ∠*M* and** ∠*O* in** Δ *MNO*.

The triangle \( \Delta MNO \) is given as an isosceles triangle with \( \angle N = 53^\circ \). In an isosceles triangle, the two base angles are equal. Since \( \overline{OM} = \overline{ON} \), the base angles are \( \angle M \) and \( \angle O \).

Let \( \angle M = \angle O = x \).

The sum of the angles in any triangle is always \( 180^\circ \). Therefore, we have:

\[
x + x + 53^\circ = 180^\circ
\]

Simplifying this equation:

\[
2x + 53^\circ = 180^\circ
\]

\[
2x = 180^\circ - 53^\circ = 127^\circ
\]

\[
x = \frac{127^\circ}{2} = 63.5^\circ
\]

So, the measures of the angles are:

- \( \angle M = 63.5^\circ \)
- \( \angle O = 63.5^\circ \)
- \( \angle N = 53^\circ \)

Would you like further details or have any questions?

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Here are 5 related questions for further exploration:

1. How would the angles change if \( \angle N \) were different?
2. What is the sum of the angles in any quadrilateral?
3. Can you determine the side lengths of \( \Delta MNO \) if you know one side length and the angles?
4. How does the type of triangle affect the relationship between its angles?
5. What are the properties of an equilateral triangle?

**Tip:** In any triangle, the exterior angle is equal to the sum of the two opposite interior angles. This can be a helpful property when solving problems involving triangle angles.

Discover how to find the measures of angles M and O in triangle MNO, given that triangle MNO is isosceles with angle N equal to 53 degrees. Learn about the properties of isosceles triangles and how to apply the sum of angles in a triangle theorem. Suitable for students in Grades 7-9.

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